American Option Pricing Under Time-Varying Rough Volatility: A Signature-Based Hybrid Framework

ArXiv ID: 2508.07151 “View on arXiv”

Authors: Roshan Shah

Abstract

We introduce a modular framework that extends the signature method to handle American option pricing under evolving volatility roughness. Building on the signature-pricing framework of Bayer et al. (2025), we add three practical innovations. First, we train a gradient-boosted ensemble to estimate the time-varying Hurst parameter H(t) from rolling windows of recent volatility data. Second, we feed these forecasts into a regime switch that chooses either a rough Bergomi or a calibrated Heston simulator, depending on the predicted roughness. Third, we accelerate signature-kernel evaluations with Random Fourier Features (RFF), cutting computational cost while preserving accuracy. Empirical tests on S&P 500 equity-index options reveal that the assumption of persistent roughness is frequently violated, particularly during stable market regimes when H(t) approaches or exceeds 0.5. The proposed hybrid framework provides a flexible structure that adapts to changing volatility roughness, improving performance over fixed-roughness baselines and reducing duality gaps in some regimes. By integrating a dynamic Hurst parameter estimation pipeline with efficient kernel approximations, we propose to enable tractable, real-time pricing of American options in dynamic volatility environments.

Keywords: American option pricing, rough volatility, signature method, Hurst parameter, Random Fourier Features, Equity Indices

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 5.5/10
• Quadrant: Holy Grail
• Why: The paper employs advanced mathematical concepts like rough-path theory, signature methods, and fractional Brownian motion with detailed formulas and derivations, indicating high mathematical complexity. While it presents empirical tests on S&P 500 options and discusses computational constraints, the validation is limited by hardware limitations, leading to moderate empirical rigor.

  flowchart TD
    A["<b>Research Goal</b><br>American Option Pricing under<br>Time-Varying Rough Volatility"] --> B["<b>Key Methodology</b><br>Signature-Based Hybrid Framework"]
    
    B --> C["<b>Data Input</b><br>S&P 500 Equity-Index Options<br>Rolling Volatility Windows"]
    
    C --> D["<b>Computational Process</b><br>1. Estimate H(t) via<br>Gradient Boosted Ensemble<br>2. Regime Switch: Rough Bergomi vs. Calibrated Heston<br>3. RFF Acceleration for<br>Signature-Kernel Evaluation"]
    
    D --> E["<b>Key Findings/Outcomes</b><br>1. H(t) ≠ Constant: Persistent roughness violated<br>2. Adaptive Framework outperforms fixed-roughness baselines<br>3. Reduced duality gaps &<br>tractable real-time pricing"]